**Tuesday, November 7**
## MS4

Functions on Surfaces

There are many scattered data interpolation and approximation
problems that arise on surfaces, for example, pressure or
temperature on the Earth, or on the surface of an aircraft or
other vehicle. Clearly it is vital to be able to represent these
data. Most existing techniques are ad hoc or dependent on the
choice of the coordinate system (e.g., the location of the poles
on a sphere). Recent work generalized the planar Bernstein-Bezier
Theory to the sphere and similar surfaces. This offers great
potential for well founded and well understood new approximation
and interpolation techniques. The speakers will survey previous
work and discuss recent work, including their own. In particular,
they will describe the application of Bernstein-Bezier technology
on the sphere, reconstruction of scalar fields from scattered
data, derivative and curvature properties of functions defined on
surfaces, and the analogs of simplex splines on closed smooth
surfaces.
Organizer:** Peter W. Alfeld**

University of Utah

**10:30 A Bernstein-Bezier Theory on the Sphere and Similar Surfaces**
*Peter Alfeld*, University of Utah; Larry Schumaker and Marian
Neamtu, Vanderbilt University
**11:00 Simplex Splines on the Sphere and on Other Closed
Surfaces**
- Marian Neamtu, Vanderbilt University
**11:30 C1 and C2 Reconstruction of Surfaces and Scalar
Fields**
*Chandrajit Bajaj*, F. Bernardini, J. Chen, and G. Xu, Purdue
University
**12:00 Construction and Visualization of Functions
Defined on Surfaces**
*Helmut Pottmann *and K. Opitz, Vienna Technical University,
Austria

*8/28/95*